Hard chemistry question

If we have 16dm^3 at 120ºC this means we must have 0.5 moles (as 32dm^3 is 1 mole and 32/16=2)

Therefore we find that the Mr we are getting is 46/0.5=92 as (n=m/Mr)
This turns out to be double the Mr of methanol acid (which is 12+16x2+2)

This must mean there are two molecules of methanol acid somehow joined together, given the presence of OH groups in methanol acid, we can deduce this is a case of hydrogen bonding between two formic acid molecules as shown in the mark scheme (where the lone pair of electrons in Oxygen delta- is attracted to the delta+ hydrogen of the other molecule)

Thank you!
But why can't we find the moles by doing 46/46 -->1mole where the mass is 46g and the mr of methanol is 46?
Also, in the mark scheme it says mr=96 but isn't the mr=46?
Could you please let me know what you think

The mark scheme says Mr=92 which divided by two is 46.
The question is asking for you to use the data provided, which is that 46g occupy 16dm^3. To do 46/46 is to miss the point of the question, as the moles of gas would therefore be 32dm^3 instead of 16.

ok so 46g of methanoic acid is the same as 0.5 moles of methanoic acid...And then onto the mr...Isn't the mr the mass of 1 mole of methanoic acid molecules? Using the periodic table, the mass of 1 mole of methanoic acid molecules is 46. So what does the 92 we get from doing 46/0.5 mean? What is 92 the mr of?

it is the Mr of two molecules of methanoic acid put together, this is due to them bonding through hydrogen bonds.

Thanks
But how do you know the mass of methanoic acid divided by the moles of methanoic acid gives the mass of two molecules of methanoic acid put together.
When you divide the total mass of X molecules by the total moles of X molecules, you get the mass of one mole of X molecules which is otherwise known as the Mr.
So taking X as methanoic acid :
Total mass of methanoic acid molecules=46g Total moles of methanoic acid molecules= 0.5
46/0.5 -->92 so this is the mass of one mole of methanoic acid molecules or in other words this is the total mass of 6.02214086 × 10²³ molecules of methanoic acid. This is because the mass of 1 mole of X is equivalent to the total mass of 6.02214086 × 10²³ molecules of X.
So I am confused - could you please let me know your thoughts

Your confusion is that you have the wrong definition of Mr. We define Mr from the mass of the elements which make the compound relative to Carbon-12. This means to find the Mr (which is a constant) of methanoic acid, we add the relative molecular masses of its constituent elements (one carbon, two oxygen and two hydrogen) to get 46.
When we do this question, we work backwards from the fact that any mole of gas occupies the same volume at a certain temperature. This leads us to find that the Mr we "theoretically get" is double that of a single molecule of methanoic acid.

However, a single molecule of methanoic acid does not weigh 46g.
A mole of methanoic acid molecules weighs 46g. Isn't this correct?
So I don't understand where you got a single molecule of methanoic acid from?
Sorry for being such a bother - this question has really messed with my head

However, a single molecule of methanoic acid does not weigh 46g.
A mole of methanoic acid molecules weighs 46g. Isn't this correct?
So I don't understand where you got a single molecule of methanoic acid from?
Sorry for being such a bother - this question has really messed with my head

you're on the right track. I'll have a go at giving an explanation.

From the data you're given you know that you have 46g of methanoic acid, and you can add up the atomic masses to work out that methanoic acid has Mr=46 g/mol

So then you can hopefully work out that you have 1 mole of methanoic acid molecules.

It is really hard to explain it online like this. Try asking your chemistry teacher, if you go over my first explanation and do it yourself it should make sense

Thank you so much for the reply! I really appreciate it and I think I am nearly there with the understanding. Could you please help me understand some bits I am stuck on?

The question says "46g of methanoic acid vapour are found to occupy 16dm^3 at 120degress and room pressure".
So, 46g of methanoic acid vapour has a volume of 16dm^3.
The Mr of methanoic acid vapour is the mass of one mole of methanoic acid vapour molecules. Using the periodic table, we get the Mr of methanoic acid vapour as 46g/mol.
We then do moles=mass/mr --> 46/46=1 ...so 1 mole of methanoic acid vapour molecules has a volume of 16dm^3. This is the same as saying 46g of methanoic acid vapour molecules has a volume of 16dm^3 which is implied by the first line of the question.

However, the bit in bold contradicts with this part of the question-->"One mole of molecules of a gas at 120degrees and room pressure occupies 24dm^3"

Where have I went wrong in my understanding here?

I would really really appreciate your thoughts on this. Sorry if I happen to repeat something which you explained before.

what you say is true, the contradiction you mention is the whole point of the question. You are supposed to notice that contradiction and then realise that something else must be going on.

You have clearly realised that the first part of the question tells you that 1 mole here occupies 16dm3 but the second part tells you it ought to occupy 32dm3.

so the question is, why is your gas occupying half the volume it should. Hopefully you might know the ideal gas equation

pV=NkT

so we have found that Volume is half what we expect, this could be explained by 3 possibilities, thinking of the equation above.

Either 1.pressure could be double what we thought (but the question tells you that's not the case)

2.The Temperature could be half what we thought (but the question tells you the Temperature)

3.The final possibility is that the number of particles could be half what we thought it was.

So how could there be half the number of particles? the answer is, that the particles pair up, so the gas occupies only half the volume.

Imagine I had 1 mole of Hydrogen atoms, they would occupy 32dm3 at this temp. and pressure.

If they suddenly all reacted to form H2 molecules, we'd now have half as many particles (each one being twice the size of what it was before) and they would therefore occupy half the volume.

So, 1 mole of individual methanoic acid molecules would occupy 32dm3

1 mole of methanoic acid molecules that have paired up, means half a mole of methanoic acid dimers so occupies 16dm3.

Also if you have asked your teacher and they have said they don't understand the question then they shouldn't be teaching Chemistry.